Cooperative deformation of carboxyl groups in functionalized carbon nanotubes

Arun K. Nair, Zhao Qin, Markus J. Buehler

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Functionalized carbon nanotubes have tremendous potential for nanotechnology applications such as in the fabrication of polymeric carbon fibers. However, approaches to design carbon nanotube structures by using functional groups as glue and carbon nanotubes as stiff building blocks to reach superior mechanical strength and toughness at the fiber level with limited amount of materials remains poorly understood. Inspired by the outstanding mechanical properties of spider silk, here we present a bio-inspired structural model of carbon nanotube based fibers connected by weak hydrogen bonds (H-bonds) formed between functional carboxyl groups as the molecular interface. By applying shear loading, we study how the deformation of H-bonds in functional groups is affected by the structural organization of the carboxyl groups, as well as by the geometry of constituting carbon nanotubes. The analysis of H-bond deformation fields is used to compute the extent of significant deformation of inter-CNT bonds, defining a region of cooperativity. We utilize an exponential function (exp (-x/ξ)) to fit the deformation of H-bonds, with the cooperative region defined by the parameter ξ, and where a higher value of ξ represents a weaker exponential decay of displacements of carboxyl groups from the point where the load is applied. Hence, the parameter ξ characterizes the number of carboxyl groups that participate in the deformation of CNTs under shear loading. The cooperativity of deformation is used as a measure for the utilization of the chemical bonds facilitated by the functional groups. We find that for ultra-small diameter CNTs below 1 nm the external force deforms H-bonds significantly only within a relatively small region on the order of a few nanometers. We find that the mechanical properties of carbon nanotube fibers are affected by the organization of H-bonds in functional carboxyl groups. Both, the grouping of functional groups into clusters, and a specific variation of the clustering of functional groups along the CNT axis are shown to be potential strategies to improve the cooperativity of deformation. This allows for a more effective utilization of functional groups and hence, larger overlap lengths between CNTs in fibers. The effect of structural organization of functional groups is not only significant in very small diameter CNTs, but also in larger diameter CNTs as they are most commonly used for engineering applications. Notably larger-diameter CNTs naturally show a larger cooperative deformation range. Our model can be applied to other functional groups attached to CNTs, and could in principle also include strong bonds such as covalent or ionic bonds, or other weak bonds such van der Waals forces or dipole-dipole interactions.

Original languageEnglish (US)
Pages (from-to)2418-2423
Number of pages6
JournalInternational Journal of Solids and Structures
Issue number18
StatePublished - Sep 15 2012
Externally publishedYes


  • Bio-inspired
  • Carbon nanotubes
  • Cooperativity
  • Deformation
  • Fiber
  • Functionalization
  • H-bonds
  • Mechanical properties

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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